Application of Derivatives 2 Question 20
20. The set of all $x$ for which $\log (1+x) \leq x$ is equal to ….. .
(1987, 2M)
Show Answer
Answer:
Correct Answer: 20. (c)
Solution:
- Let $f(x)=\log (1+x)-x$
$\therefore f(x)$ is increasing for $-1<x<0$.
$$ \begin{array}{lrl} \Rightarrow & f(x) & <f(0) \\ \Rightarrow & \log (1+x) & <x \end{array} $$
Again, $f(x)$ is decreasing for $x>0$.
$$ \begin{array}{ll} \Rightarrow & f(x)<f(0) \\ \Rightarrow & \log (1+x)<x \\ \therefore & \log (1+x) \leq x, \forall x>-1 \end{array} $$
